Nancy’s first managerial stint in Europe – having moved from Major League Soccer (MLS) side Colombus Crew – began with defeats by title rivals Hearts and Roma in the Europa League, before a 3-1 loss to St Mirren in the Scottish League Cup final.
Their latest defeat at Tannadice left Celtic six points behind Premiership leaders Hearts, albeit with a game in hand.
“The thing is it’s tough to come and try to impose your philosophy and your identity at a club maybe – I don’t know because I haven’t watched many games – playing another way,” Henry said.
“Right now it’s too early, and I do think he can turn it around. He is a great guy and has a great mind.
“It’s not working at the moment and obviously it doesn’t look great. But he’s a friend of mine, so I am going to be biased.
“You don’t want any coach to lose their job that early. It doesn’t make sense to me.”
Nancy, who led Columbus Crew to the MLS Cup in 2023 and the Leagues Cup the following year, was named MLS coach of the year in 2024.
He will search for his first points as Celtic manager when his side host Aberdeen in the Scottish Premiership on Sunday (15:00 GMT).